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What do you mean by smallest breed? All aquatic turtles are generally the same size. They grow accordingly to the enclosure they're placed in.

I have a Southern Yellow Painted Turtle that lives in my community Tetra/Danio tank, he is only 5 inches long, yet he's been in there for 5 years.

I also have Red-Eared Slider Turtles in my outdoor 4000 gallon Koi pond, they have only been there 3 years, but they are nearly 10 inches long.

How much are you willing to spend per turtle? I advise you that while your turtle will be fine on his own, he would enjoy the company of at least one other turtle, preferably female.

DO NOT GET ANY SNAPPING TURTLES!
Generally, they get huge, and then start reeking havoc as they eat fish and uproot plants digging in the substrate.

I recommend either getting Painted or Slider turtles. They are the most common in the hobby and the easiest to care for.

But to answer your question, the Musk turtle, or Sternotherus odoratus, is the smallest freshwater turtle, it grows to about 4-5 inches long. I don't recommend this turtle though, as it fouls up the water faster than other species and generally does not smell good. (Turtles don't smell good but this guy smells worse)

CYCLE WITHOUT FISH FOR THE LOVE OF POSEIDON

Currently in the process of moving all of my tanks, everything is down for now!

right now i have a red eared slider in a 20 gallon long tank with waterfall bamboo plants and growing some aquarium water lilies. trooper is only one inch and was wandering what do you think about adding one algae eater with him? also how big is your tank with the painted turtle and fish

How long have you been thinking about this because as AVN said they fould up your water fast and some species can live till their 30's, might be something to think about because the last thing i and probably everyone else wants is more sliders in the lakes, rivers, etc.

Like fish, turtles need appropriate space to grow. It's not fair to stunt their growth by keeping them in a small enclosure. That said, eventually you'd need a LARGE tank, we're talking 75g+ and preferably long. Turtles need to be able to swim, and also have space to be fully dry. They need UV lighting or their shell will rot and they will die. They have a long lifespan when cared for properly and the decision to acquire one shouldn't be taken lightly.
I'd considered one at one point, but after learning about their requirements and lifespan I decided against it. I think it's a shame that they're sold as pets as the majority of people can't/don't/won't meet their requirements and many turtles die while they're still adolescents because of it.